Yes Civilians can wear and buy body armor legally as long as the person is not a convicted felon that has done something serious.
If you have a good record and haven't been in trouble with the law before and have no felonies on your record then yes you can legally purchase body armor online or anywhere else that sells it.
You can also legally wear that body armor in public for your safety if you want too.
However although body armor such as bullet proof vests can protect you from getting shot in at least the area the bullet proof vets cover they are extremely uncomfortable and can cause chafing around your neck etc.
They are also hot to wear when the temperature is hot.